The ratio of the specific heats frac{C_p}{C_v | vedclass

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(C) For $n$ degrees of freedom,the molar heat capacity at constant volume is given by $C_v = \frac{n}{2}R$.From Mayer's relation,we know that $C_p - C

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$1 + \frac{2}{n}$

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(C) For $n$ degrees of freedom,the molar heat capacity at constant volume is given by $C_v = \frac{n}{2}R$.From Mayer's relation,we know that $C_p - C_v = R$,which implies $C_p = C_v + R$.Substituting the value of $C_v$,we get $C_p = \frac{n}{2}R + R = R\left(\frac{n}{2} + 1\right) = R\left(\frac{n+2}{2}\right)$.The ratio of specific heats $\gamma$ is defined as $\gamma = \frac{C_p}{C_v}$.Substituting the expressions for $C_p$ and $C_v$,we get $\gamma = \frac{R(\frac{n+2}{2})}{\frac{n}{2}R} = \frac{n+2}{n} = 1 + \frac{2}{n}$.

List-$I$	List-$II$
$A$. Triatomic rigid gas	$I$. $\frac{C_P}{C_V} = \frac{5}{3}$
$B$. Diatomic non-rigid gas	$II$. $\frac{C_P}{C_V} = \frac{7}{5}$
$C$. Monoatomic gas	$III$. $\frac{C_P}{C_V} = \frac{4}{3}$
$D$. Diatomic rigid gas	$IV$. $\frac{C_P}{C_V} = \frac{9}{7}$

The ratio of the specific heats $\frac{C_p}{C_v} = \gamma$ in terms of degrees of freedom $(n)$ is given by

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